General four-step discrete-time zeroing and derivative dynamics applied to time-varying nonlinear optimization

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:347

Article

Zhang, Yunong¹  He, Liu¹  Hu, Chaowei^1,2  Guo, Jinjin¹  Li, Jian¹  Shi, Yang¹ 

[1] Sun Yat Sen Univ, Sch Informat Sci & Technol, Guangzhou 510006, Guangdong, Peoples R China

[2] Huaqiao Univ, Coll Informat Sci & Engn, Xiamen 361021, Peoples R China

关键词: Time-varying nonlinear optimization;    Derivative dynamics;    Zeroing dynamics;    Zhang et al. discretization;    General ZeaD formula;   

DOI  :  10.1016/j.cam.2018.08.017

来源: Elsevier

【 摘 要 】

Time-varying nonlinear optimization (TVNO) problems are considered as important issues in various scientific disciplines and industrial applications. In this paper, the continuous-time derivative dynamics (CTDD) model is developed for obtaining the real-time solutions of TVNO problems. Furthermore, aiming to remedy the weaknesses of CTDD model, a continuous-time zeroing dynamics (CTZD) model is presented and investigated. For potential digital hardware realization, by using bilinear transform, a general four-step Zhang et al discretization (ZeaD) formula is proposed and applied to the discretization of both CTDD and CTZD models. A general four-step discrete-time derivative dynamics (general four-step DTDD) model and a general four-step discrete-time zeroing dynamics (general four-step DTZD) model are proposed on the basis of this general four-step ZeaD formula. Further theoretical analyses indicate that the general four-step DTZD model is zero-stable, consistent and convergent with the truncation error of O(g(4)), which denotes a vector with every entries being O(g(4)) with g denoting the sampling period. Theoretical analyses also indicate that the maximal steady-state residual error (MSSRE) has an O(g(4)) pattern confirmedly. The efficacy and accuracy of the general four-step DTDD and DTZD models are further illustrated by numerical examples. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

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